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This paper establishes an exact correspondence between neural network training and Hamilton-Jacobi initial-value problems, unifying deep learning architectures through a deformation parameter.
The paper introduces beignet, a PINN architecture that replaces random Fourier features with a trainable multi-resolution Fourier feature pyramid, achieving higher accuracy and computational efficiency on PDE benchmarks.
This paper introduces breakeven complexity, a metric to determine when neural PDE solvers become cost-effective compared to traditional numerical solvers. The framework uses scaling laws to allocate training budgets and evaluates multiple neural solvers on diverse PDE benchmarks.
This paper proposes a spatially correlated curriculum learning framework for Physics-Informed Neural Networks (PINNs) that improves training stability and solution accuracy by leveraging spatial correlations among subregions, addressing issues like high-dimensional non-convex loss landscapes and imbalanced multi-objective constraints.
This paper extends Port-Hamiltonian Neural Networks (PHNNs) to partial differential equations (PDEs) for learning nonlinear string dynamics from data. The approach recovers both the Hamiltonian and dissipation, outperforming non-physics-informed baselines in accuracy and interpretability.